VCE Mathematical Methods/Exam One Practice One
Reading Time: 15 minutes
Writing Time: 60 minutes
- Students are permitted to use: pencils, pens, highlighters, erasers, sharpeners, rulers, protractors, set-squares, aids for curve sketching
- Students are NOT permitted to use: blank sheets of paper, white-out, any type of technology
- Any diagrams used are NOT drawn to scale unless otherwise indicated
- Students must answer all the questions in the space provided
- In questions where more than one mark is available, appropriate working MUST be shown
- When instructed to use calculus, an appropriate derivative or anti-derivative MUST be shown
Question 1 
(a) Given , solve for x.
(b) If and state the transformations required to change g into f
[1 + 2 = 3 marks]
Question 2 
Let and .
(b) Hence factorise P(x) given that .
(c) Hence sketch the graph of P
[2+2+2 = 6 marks]
Question 3 
Let . Use calculus to find the co-ordinates of the stationary point.
Question 4 
A garden path can be modelled with the equation where .
(a)Sketch the garden path over the domain specified.
(b) If the x-axis represents a fence, use calculus to determine the area between the path and the fence.
[2+2 = 4 marks]
Question 5 
State the equations of the tangent and the normal of the function when
Question 6 
Shirley either eats lamingtons or a muesli bar for morning tea. If Shirley eats lamingtons one day, then the probability she will eat lamingtons the next day is 0.5. If Shirley eats a muesli bar one day, the probability that she will eat a muesli bar the next day is 0.3. If Shirley eats a muesli bar on Tuesday, what is the probability she will eat lamingtons on Thursday?